Use the quotient-remainder theorem with divisor equal to 2 to prove the following statement. a. The square of any integer can be written in one of the two forms 4k or 4k+ 1 for some integer k.

Please read the enswer below

Step-by-step explanation:

The quotient-remainder theorem establishes that given an integer n, there are unique integers d and r, with 0≤r<d, and such that:

q: the quotient

d: the remainder

d: divisor = 2

By the quotient-remainder theorem with divisor 2, you have:

n = 2q

n = 2q + 1

Then, for both cases you have:

  (the square of an integer with divisor 2 is 4k)

with

but 2q + 1 = n

where you have taken   (the product 2qn is another integer)

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500

6,250

step-by-step explanation:

to get the area, multiply 360 by 160.(57,600)

to find out how many bags of fertilizer it will take, first figure out how many square feet one bag can hold. divide 1000 by 8(125) to get the unit rate(how many square feet one pound of fertilizer can hold)and multiply it by 50(6250). if i haven't made a mistake, that is the answer.